Cross multiplication is a common method used when working with fractions. But can you use it to compare fractions? Absolutely! This article will explain how cross multiplication works and demonstrate how to use it to determine which fraction is larger or if they are equivalent.
Understanding Cross Multiplication
Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. Let’s say we have two fractions: a/b and c/d. Cross multiplying would look like this:
a x d = b x c
This process helps establish a relationship between the two fractions, allowing for comparison.
Comparing Fractions with Cross Multiplication
The result of cross multiplication tells us if two fractions are equal or which one is greater.
- If a x d = b x c: The fractions are equivalent (a/b = c/d).
- If a x d > b x c: The fraction a/b is greater than c/d.
- If a x d < b x c: The fraction a/b is less than c/d.
This method is particularly helpful when dealing with fractions that are difficult to compare visually or by finding a common denominator.
Example: Comparing Fractions
Let’s compare 4/26 and 7/32 using cross multiplication:
- 4 x 32 = 128
- 7 x 26 = 182
Since 182 > 128, we can conclude that 7/32 is greater than 4/26. Remember, the product of the cross multiplication corresponds to the original fraction. 128 represents 4/26 and 182 represents 7/32.
Solving for Unknowns with Cross Multiplication
Beyond comparing fractions, cross multiplication is a powerful tool for solving equations involving fractions with an unknown variable.
Consider the equation 9/16 = x/27:
- Cross multiply: 9 27 = 16 x
- Simplify: 243 = 16x
- Solve for x: x = 243/16
This demonstrates how cross multiplication simplifies solving for unknown variables in fraction equations.
Conclusion
Cross multiplication is a valuable technique for comparing fractions and solving equations involving fractions. It provides a clear and efficient way to determine the relationship between two fractions and find the value of unknown variables. Whether you’re comparing simple or complex fractions, cross multiplication offers a reliable method for arriving at the correct answer.
